On red shifs in the transition region and corona

0.37 MB·English

by  Viggo H. Hansteen

Mem.S.A.It.Vol.1,1
(cid:13)c SAIt 2008 Memoriedella
On red-shifts in the Transition Region and
Corona
V.H.Hansteen1,2,3,4,H.Hara2,B.dePontieu3,andM.Carlsson1,4
0
1
0 1 Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-
2 0315Oslo,Norway
2 National Astronomical Observatory of Japan, 2—21–1 Oswawa, Mitaka, Tokyo 181–
n
8588,Japan
a
3 LockheedMartinSolar&AstrophysicsLab,Org.ADBS,Bldg.252,3251HanoverStreet
J
PaloAlto,CA94304USA
6
4 Center of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern,
2
N-0316Oslo,Norwaye-mail:[email protected]

]
R
S Abstract. Wepresentevidencethattransitionregionred-shiftsarenaturallyproducedin
. episodicallyheatedmodelswheretheaveragevolumetricheatingscaleheightliesbetween
h thatofthechromosphericpressurescaleheightof200kmandthecoronalscaleheightof
p 50Mm.Inordertodosowepresentresultsfrom3dMHDmodelsspanningtheuppercon-
- vectionzoneuptothecorona,15Mmabovethephotosphere.Transitionregionandcoronal
o
heatinginthesemodelsisdueboththestressingofthemagneticfieldbyphotosphericand
r
t convection‘zonedynamics,butalsoinsomemodelsbytheinjectionofemergingmagnetic
s
flux.
a
[
Keywords.Sun:transitionregion—Sun:corona—Sun:atmosphericmotions

1
v
9
1. Introduction els where transition region structure is dom-
6
7 inated by thermal conduction from overly-
Observations of the upper chromosphere and
4 ing coronal structures. The average red-shift
of the transition region point to a number of
. has been explained by a variety of models,
1 mysteries that have yet to be adequately ex-
e.g.Athay&Holzer (1982) and Athay (1984)
0 plained.
0 conjectured that red-shifts were due the re-
Chief among these are the rise in the dif-
1 turn of previously heated spicular material,
ferential emission measure (DEM) at temper-
: on the other hand Hansteen (1993) argued
v atures below 105 K (Mariska 1992) and the
that nanoflareinduced waves generatedin the
i ubiquitousaveragered-shiftfoundintransition
X coronacouldproducea netred-shiftintransi-
region lines (Chaeetal. 1998; Peter&Judge
r tionregionlines.
a 1999) In short, the rise in the DEM at lower
MorerecentlyPeteretal.(2006)foundthat
transition region temperatures indicates that
3dnumericalmodelsthatspanthephotosphere
much more plasma is emitting in this tem-
to corona produce red-shifts in transition re-
perature range than is accounted for by mod-
gion lines. In these models coronal heating is
Sendoffprintrequeststo:V.H.Hansteen duetheJouledissipationofcurrentsproduced
2 Hansteenetal.:Red-ShiftsintheTR
asthemagneticfieldisstressedandbraidedby
photosphericmotions, but the ultimate source
of the red-shifts is not clear. Spadaroetal.
(2006) used 1d models of coronal loops to
showthatred-shifts,andtheobservedDEMat
temperatures below 105 K could be the result
oftransientheatingneartheloopfootpoints.
In this work we extend the work of Peter
et al. and Spadaro et al. to show that transi-
tion region red-shifts are naturally produced
in episodically heated models where the av-
erage volumetric heating scale height lies be-
tweenthatofthechromosphericpressurescale
heightof200kmandthecoronalscaleheight
of50Mm.
Fig.1. Vertical magnetic field B in the pho-
2. 3dsimulationsofthesolar z
tosphere and magnetic field lines that reach
atmosphere
the corona (in blue). The image is from time
WesolvetheMHDequationsusingBIFROST t=2700sintheA2simulation.
(Gudiksenetal. 2010). This code employs a
high-order finite difference scheme and in-
cludesahigh-orderartificialviscosityinorder lines as well as the injection of new “emerg-
to maintain numerical stability. These terms ing” magnetic flux at the lower boundary.
are also the source of magnetic and viscous These processes have been described earlier
heating. Non-grey, optically thick radiative in the contextof numericalsimulations of the
lossesincludingtheeffectsofscatteringarein- outersolaratmosphere(Gudiksen&Nordlund
cluded,asareopticallythinradiativelossesfor 2005; Hansteen 2004; Hansteen&Gudiksen
the upper chromosphere and corona and con- 2005;Hansteenetal.2007)andalsoincluding
ductionalongthefieldlinesinthecorona. flux emergence (Mart´ınez-Sykoraetal. 2008,
2009).
Threeofthemodelsarecomprisedof512×
2.1.Simulationdescription
512×325 points spanninga region of 16.6×
In this paper we will use results from four 16.6×15.5Mm3.Thesemodelsdifferintheir
3dsimulationsofthesolaratmosphere.These total unsigned magnetic flux, the weak field
modelsspantheregionfrom1.4Mmbelowthe model henceforth named “A1” has h|Bz|i =
photosphereto14Mmabovethephotosphere, 20Ginthephotosphere.Ontheotherhand,the
and thus include the upper convection zone, strongerfieldmodel,named“A2”hash|Bz|i≈
the photosphere, chromosphere, transition re- 100G.Inaddition,inthestrongerfieldmodel
gionandthe(lower)corona.Photosphericand a flux sheet is injected at the bottom bound-
lower chromospheric radiative losses are bal- ary. Finally, the “A3” model is initially iden-
anced by an in-flowing heat flux at the bot- tical to A2 butwith very little flux injected at
tom boundary.The chromosphereandregions the bottom boundary.The A1 and A2 models
above are maintained by the dissipation of have been run for 1 hour solar time while the
acoustic shock waves that are generated in A3modelforroughly45minutes.
theconvectionzoneandphotosphere,butper- Thefourthmodel,“B1”,haslowerresolu-
haps more importantly by the dissipation of tion—256×128×160points—andspansa
the Poynting flux that is injected into the smallerregionof16.6×8.3×15.5Mm3.The
upper atmosphere. This Poynting flux arises unsigned magnetic field is of the same order,
as a result of the braiding of magnetic field but slightly weaker h|B |i ≈ 75 G, than in as
z
Hansteenetal.:Red-ShiftsintheTR 3
LineID λ[nm] log(T ) mass[amu]
max
HeII 25.63 4.9 4.0
CIV 154.82 5.0 12.0
OVI 103.19 5.5 16.0
SiVII 27.54 5.8 28.1
FeXII 19.51 6.1 55.9
FeXV 28.42 6.3 55.9
Table 1. List of lines synthesized from the
simulationsdescribed.
Fig.2.IntensityprofilesoftheCIVandSiVII
linesasfunctionsoftimefromthelowresolu-
tionsimulationB1.
in the strong field modelabove.This low res-
olutionmodelalsoincludesaninjectedemerg- putedassumingthatthelinesareopticallythin
ingfluxsheet.TheB1modelhasbeenrunfor andthattheionizationstateisinequilibrium
1hoursolartime.
hν
In figure 1 we show the vertical magnetic
I = φ (u,T )n n g(T )ds (1)
fieldinthephotospherealongwithasubsetof ν 4πZ ν g e H g
s
fieldlinesthatreachcoronalheightsintheA2
where the integration is carried out along the
simulation. This magnetic topology is typical
line of sight, orin this case verticallythrough
forthesimulationsdiscussedhere.
the box along the z axis. The line profile is
Also typical for these models is a tem-
computedassumingDopplerbroadening.
perature structure in the transition region and
Examinenowhowthelineprofilesvaryas
corona where the temperature begins to rise
a function of time at a given typical location
some 1.5 Mm above the photosphere and has
pickedmoreorlessatrandomintheB1simu-
reached1.0MKalreadyatheightsof3−4Mm.
lation. The transition region line profiles, ex-
However, the structure of the atmosphere is
emplified by C IV and Si VII representative
farfromhorizontallyhomogeneousandwefind
of the lower and upper transition region re-
very hot plasma (> 2 MK for the A2 run)
spectively, are shown in figure 2. These lines
already at heights of 1.5 Mm, while at the
showafairlysimilarevolutionwithsignificant
same timewe findcoolgaswith temperatures
variationsinlineintensity,shift,andwidthon
<10kKevenatheightsupto6Mm.
time-scalesdowntolessthanaminute.Wesee
strongred-shifteventsaccompaniedbybright-
2.2.CharacteristicsofsimulatedTRand ening such as at 18 min and at 56 min, and
coronallines a weaker blue-shifted event at 47 min. It is
clearlyevidentthatthebulkoftheCIVlineis
Let us now consider some examples of sim- red-shiftedatalmostalltimes,whiletheSiVII
ulated spectral lines formed in the transition linehaslittlenetshift.
region and corona of these models. We have The coronal line profiles, exemplified by
chosen lines that have been previously well FeXIIandFeXVareshowninfigure3.Also
observed with space borne instruments such here we find large variations in the line pa-
asSOHO/SUMERorarecurrentlyobservable rametersonseveraltimescalesincludingthose
with Hinode/EIS. These lines cover a wide shorter than 1 min. The coronallines become
spanoftemperaturein throughtheoutersolar brighter as the corona grows hotter at times
atmosphereandaresummarizedintable1. laterthan20mininthesimulation.Thestrong
ThesynthesizedintensitiesI inthevarious brightening and blue-shift seen at 47 min is
ν
EUVspectrallinesmentionedabovearecom- found to be associated with a strong heating
4 Hansteenetal.:Red-ShiftsintheTR
Fig.3. Intensity profiles of the Fe XII and
FeXVlinesasfunctionsoftimefromthelow
resolutionsimulationB1.
Fig.6. Current density squared per particle
event (the joule heating in the B1 model is (ηj2/ρ) at time t = 2810 s in simulation B1
showninfigure6,wheretheeventcausingthe
(redweakest,bluestrongest)andverticalmag-
line variation is clearly visible). Note that the
neticfieldB inthephotosphere.
z
coronallinesatthislocationarepreferentially
blue-shifted.
We can also examinethe propertiesof the ple inthe Fe XIIline intensitiesshownin fig-
lines by examining the lower order moments; ure5whichclearlydelineatethemagneticfield
the total intensity, average line shift, and av- linesthatstretchmoreorlesshorizontallybe-
erage line width. In figure 4 we show the line tween the footpointsin the form of loops. On
moments of the lower transition region C IV the other hand, the structure of line shifts are
line at time t = 2700 s in the A2 run. The verysimilarto thestructurefoundinthe tran-
leftpanelshowsthetotalintensity,themiddle sition region lines. Blue-shifts are generally
panelthelineshift,andtherightpaneltheline larger (the maximum blue-shift is −75 km/s
width. While the intensities do not obviously whilethemaximumred-shiftisonly35km/s)
reflect the topology of the magnetic field, the andconcentratedtotheloopfootpoints.Notice
lineshiftandwidtharemoreclearlyrelatedto that footpointintensities are much lower than
the field. Intense red- and blue-shiftsare gen- in the bodies of the loops between the foot-
erallyconcentratedtopositionswherethefield points, presumably as footpoint temperatures
comesupverticallyfromthechromospherebe- aretoolowtogiveemissionincoronallines.
low, i.e in the loop footpoints (see figure 1).
In the regionsbetween the footpointswe also
3. Coronalheatinginthismodel
findbothred-andblue-shiftsalignedalongthe
fieldlinesthatstretchfromthefootpointscon- Letusnowputthe“observed”lineprofilesde-
centrated in bands near x = 7 Mm and near scribed into context with the coronal heating
x=13Mm.Similarly,wefindthatthegreatest thatcharacterizesthesemodels.
line widths are found in the footpoint bands, The heating per particle (∝ j2/ρ) is con-
and the C IV lines are in generallymuch nar- centratedtocertainregionsandstructuresthat,
rower in the regions between. However, note in general, follow the magnetic field lines as
thatwealsofindsomelargelinewidthregions shown in figure 6 where the heating in the
strething in thin strings between the footpoint B1 simulation at time 2810 s. This heating is
bandsandalignedwiththefieldlinesshownin highlyirregularbothinspaceandtimebutisin
figure1. largepartconcentratedtothetransitionregion
Thepatternofintensitiesseeninthecoro- and lower corona. Note that regions of high
nal lines is quite different, as seen for exam- heating (colored in green — blue) in part are
Hansteenetal.:Red-ShiftsintheTR 5
Fig.4.Totalintensity,dopplershift,andlinewidthintheCIVlineattimet = 2700sintheA2
simulation.Thevelocityscaleisfrom−40km/s(blue)to40km/s(red).Linewidthsrangefrom
narrowblacktowideyellow/redwithamaximumof51km/s.TheaveragelineshiftintheCIV
lineis6.6km/s.
Fig.5.Totalintensity,dopplershift, andline widthinthe Fe XII lineattime t = 2700sin the
A2simulation.Thevelocityscale isfrom−40km/s(blue)to40km/s(red).Linewidthsrange
fromnarrowblacktowideyellow/redwithamaximumof76km/s.Theaveragelineshiftinthe
FeXIIlineis−2.7km/s.
alignedinlooplikestructures,inpartinlinear the heating varies continuously in time also
structures thatstretch high into the corona.In here.
addition,wefindaweakercomponent(colored
inred)which,thoughitalsofollowsthestruc-
Thus,highheatingeventsoccurinspatially
ture of the magnetic field, seems much more
localized bursts that lead to increases in the
evenlyspreadoutandspacefillingthanthere-
temperature but also large velocities. For ex-
gions of (sporadic) high heating. In time, the
ample, the large linear structure that reaches
linear regions of high heating are short lived,
highintothecorona,seeninthemiddleofthe
oforder100sorshorter.Thelinearstructures
left panel of figure 6 is the event that is visi-
sometimesalsomovehorizontallyoverathou-
ble in figure 2 as a line shift of the transition
sandkilometersorsoduringtheirlifetime.The
regionlinesattimet = 47minutesandthatis
loopshapedstructuresarelongerlived,though
also evidentin figure3 as a line shiftand, es-
6 Hansteenetal.:Red-ShiftsintheTR
Similar heating scale heights are found in
Mart´ınez-Sykoraetal. (2008, 2009). Theyare
muchgreaterthanthechromosphericpressure
scale height of 200 km while, on the other
hand, being much smaller than the transition
region scale height of 6 Mm or the 60 Mm
coronal scale height. Thus, in models where
chromospheric/coronal heating is determined
byphotosphericworkonthemagneticfield—
withorwithoutfluxemergence—wefindthat
the heating per unit mass (or equivalentlyper
particle) necessarily is concentrated towards
the transitionregionandthe low corona:Low
inthechromospheretheparticledensityisvery
high and therefore the heating rate per parti-
cle low. At the same time radiative losses are
veryefficientattheseheights,thustheplasma
easilyridsitselfofdepositedenergy.However,
since the scale height of heating (∼ 650 km)
is greater than that of the particle density (∼
200 km) in the roughly isothermal chromo-
sphere,the heatingperparticlerisesexponen-
tially with height. At some point the heating
overwhelmstheplasma’sabilitytoradiate,and
the temperature rises to coronaltemperatures,
Fig.7. Average joule heating ηj2/ρ (solid
as illustrated in figures 7. This figure shows
line) and average radiative losses L =
r the joule heating (ηj2) and radiative cooling
−n n f(T)/ρ (dot dashed line) per unit mass
e H (L = −n en f(T)) per unit mass as a func-
in the chromosphere and lower transition re- r e H
tion of height. The temperature continues to
gion (upper panel) and corona in simulation
riseuntilthermalconductionbecomeseffective
B1.Theaveragetemperatureisoverplottedfor
enoughtobalancethedepositedenergyattem-
reference(dashedline).
peraturesapproaching1MK.Thistemperature
is high enough that the density scale height
becomes much larger than the heating scale
pecially for the Fe XV line, by an increase in
heightandtheheatingperparticlethereforede-
theintensity.
creases exponentially, roughly as the heating
The concentration of heating towards the
rate(orthemagneticenergydensity)itself.
transition region and lower corona can be
understood by considering the various scale
heights involved. We find that joule heat-
4. Discussion&Conclusions
ing caused by the braiding of the magnetic
fielddecreasesexponentiallywithheightfrom Thus simulations of this sort lead to a coro-
the upper photosphere with a scale height nal heating model where sporadic heating of
that is closely related to the scale height of material occurs mainly in the vicinity of the
the magnetic energy density (B2/2µ ). This upper chromosphere, transition region, and
0
is the same result as found earlier in the lower corona. When a heating event occurs
Gudiksen&Nordlund (2005) model (see fig- in the upper chromosphere or transition re-
ure 7 of that paper), where a heating scale gioncoolermaterialis rapidlyheatedtocoro-
height of order 650 km was found in the nal temperatures. When heating occurs in the
chromosphere, rising to 2.5 Mm in the low lowercoronathethermalconductionincreases
corona and 5 Mm in the extended corona. rapidly with rising coronal temperatures and
Hansteenetal.:Red-ShiftsintheTR 7
foundinthetransitionregionandlowercorona
asshowninfigure8.Averagelineshiftsfound
insimulationB1arerelativelyconstant,show-
ingalargeapparentdownflowinthetransition
region and a smaller apparentupflow at coro-
nal temperatures. These line shifts represent
anactualmaterialflow,onaveragematerialis
flowing away from the temperature of some
7×105Kwithamaximumdownwardvelocity
of some 5 km/sat 3×104 K and a maximum
upward velocity of 2 km/s at 1 MK as shown
in the lower panel of figure 8. The line shifts
reflectthisflowtrendfairlyaccuratelybutdue
totheweightingofthelineprofilewithdensity
(∝ n n the line shifts are exaggerated in the
e H
transitionregion.Wefindthattheaverageline
shiftinthecoolesttransitionregionlines,HeII
and C IV are of order 7−8 km/s. The O VI
line is also shifted, but less, with an average
that lies near 4 km/s. The upper transition re-
gionSiVIIlineisinitiallyblue-shifted,butas
timepassesinthesimulationthelineshiftde-
creasestowardszeroandisslightlyred-shifted
at the end of the run. Finally the Fe XII line
hasanaveragelineshiftofzeroinitiallybutis
Fig.8. Average line shift in the B1 model as
slightly blue-shifted at the end of the simula-
a functionof timeforthe linesoftable 1(up-
tionrun.
per panel): He II (dotted), C IV (solid), O VI
Notethatthoughanetred-shiftisobserved
(dash),SiVII(dashdot),andFeXII(dashdot
intransitionregionlineswhichcorrespondsto
dot dot). The lower panel shows the average
amaterialflowoutofthetransitionregion,the
lineshiftsandtheaveragevelocity(dashed)as
coronalmassisactuallyconstantorgrowingin
afunctionoflogtemperatureinsimulationB1.
thesesimulations.Thus,materialdoesnotflow
Theerrorbarsintheaveragelineshiftaregiven
into the corona through the transition region.
bythestandarddeviationintheaverageveloc-
Rather,morematerialisheatedrapidlytohigh
itiesasafunctionoftime.
temperatures than can be supported, and this
materialissubsequentlypushedoutoftheup-
the cooler chromospheric material just below pertransitionregionintothecoronaandchro-
canbeheatedbyathermalwave.Itisourcon- mosphere.
tentionthattheseprocesseshappensufficiently Further support for this scenario dominat-
rapidlythatmaterialisheatedmoreorless“in ing the computed models is shown in fig-
place”beforeithastimetomove.Thus,newly ure 9 where we plot the correlation between
heatedtransitionmaterialwillbecharacterized the red-shift measured in the C IV transition
by higher than hydrostatic pressures, and we region line and the maximum downward ori-
expect,onaverage,tofindaplugofhighpres- ented pressure gradient (dp/dz)/ρ. The figure
surematerialthatseekstoexpandintoregions showsthathighred-shiftoccursinregionswith
oflowerpressureoneitherside;downwardsto- a large downward directed pressure gradient.
wardsthechromosphereandupwardstowards Notethatfigure9alsoshowsthatafairlylarge
thecorona. population of large downward directed pres-
The flows away from the high pressure suregradientsco-existwithlineshiftsthatare
plug are reflected in the average velocities closetozero.Thispopulationisrepresentative
8 Hansteenetal.:Red-ShiftsintheTR
Acknowledgements. V.H.H. thanks the NAOJ for
hospitality during the summer of 2009. This
reasearchwassupportedtheEuropeanCommission
funded Research Training Network SOLAIRE.
It was also supported from grants of comput-
ing time from the Norwegian Programme for
Supercomputing from the Norwegian Research
CouncilHinodegrant.
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